Pamukkale University
University is the guide to life
Welcome to PAU;
Prospective Student
Our Students
Our Staff
TR
Information Package & Course Catalogue
Home Page
About University
Name And Address
Acedemic Authorities
General Discription
Academic Calendar
General Admission Requirements
Recognition of Prior Learning
General Registration Procedures
ECTS Credit Allocation
Academic Guidance
Information For Students
Cost Of Living
Accommodation
Meals
Medical Facilities
Facilities for Special Needs Students
Insurance
Financial Support for Students
Student Affairs
Learning Facilities
International Programs
Language Courses
Internships
Sports Facilities and Leisure Activities
Student Associations
Practical Information for Mobile Students
Degree Programmes
THIRD CYCLE - DOCTORATE DEGREE
THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES
MATHEMATICS DEPARTMENT
1441 Mathematics
Course Information
Course Learning Outcomes
Course's Contribution To Program
ECTS Workload
Course Details
Print
COURSE INFORMATION
Course Code
Course Title
L+P Hour
Semester
ECTS
MAT 544
TENSOR GEOMETRY AND APPLICATIONS I
3 + 0
1st Semester
7,5
COURSE DESCRIPTION
Course Level
Doctorate Degree
Course Type
Elective
Course Objective
The goal of the course is to make applications about lagrange systems using tensor on manifolds.
Course Content
Introduction toTensor Geometry, Non-Euclidean Geometries, Geometry of Space Curves, Rn Geodesics, Geodesic Coordinates, Tensor Derivatives, Fundamental Concepts on Analytic Mechanics, Applications of Lagrange Equations.
Prerequisites
No the prerequisite of lesson.
Corequisite
No the corequisite of lesson.
Mode of Delivery
Face to Face
COURSE LEARNING OUTCOMES
1
Learns tensor geometry, knows geometry of space curves.
2
Realized Rn geodesics, geodesic coordinate and tensor derivatives.
3
Learns the basic concepts and Lagrange equations applications.
COURSE'S CONTRIBUTION TO PROGRAM
PO 01
PO 02
PO 03
PO 04
PO 05
PO 06
PO 07
PO 08
LO 001
5
4
4
LO 002
4
5
5
4
LO 003
5
4
4
5
Sub Total
14
13
9
13
Contribution
5
0
4
3
0
0
0
4
ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
Activities
Quantity
Duration (Hour)
Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)
14
3
42
Hours for off-the-classroom study (Pre-study, practice)
14
7
98
Assignments
1
5
5
Mid-terms
1
15
15
Final examination
1
35
35
Total Work Load
ECTS Credit of the Course
195
7,5
COURSE DETAILS
Select Year
All Years
2022-2023 Fall
2011-2012 Fall
2010-2011 Spring
2010-2011 Fall
2009-2010 Fall
Course Term
No
Instructors
Details
2022-2023 Fall
1
CANSEL AYCAN
Details
2010-2011 Fall
1
MEHMET TEKKOYUN
Details
2009-2010 Fall
1
MEHMET TEKKOYUN
Print
Course Details
Course Code
Course Title
L+P Hour
Course Code
Language Of Instruction
Course Semester
MAT 544
TENSOR GEOMETRY AND APPLICATIONS I
3 + 0
1
Turkish
2022-2023 Fall
Course Coordinator
E-Mail
Phone Number
Course Location
Attendance
Prof. Dr. CANSEL AYCAN
c_aycan@pau.edu.tr
FEN A0316
%70
Goals
The goal of the course is to make applications about lagrange systems using tensor on manifolds.
Content
Introduction toTensor Geometry, Non-Euclidean Geometries, Geometry of Space Curves, Rn Geodesics, Geodesic Coordinates, Tensor Derivatives, Fundamental Concepts on Analytic Mechanics, Applications of Lagrange Equations.
Topics
Weeks
Topics
1
structure of manifold
2
system of frenets
3
frenet roofs
4
curvatures
5
tensors
6
christoffel symbols
7
mechanical systems
8
applications of mechanical systems
9
midterm exam
10
jet manifolds
11
jet bundles and its applications
12
minimal surfaces
13
trend lines, curvatures
14
fınal exam
Materials
Materials are not specified.
Resources
Resources
Resources Language
yüksek diferensiyel geometriye giriş, H.H Hacısalihoğlu
Türkçe
Course Assessment
Assesment Methods
Percentage (%)
Assesment Methods Title
Final Exam
50
Final Exam
Midterm Exam
50
Midterm Exam
L+P:
Lecture and Practice
PQ:
Program Learning Outcomes
LO:
Course Learning Outcomes
{1}
##LOC[OK]##
{1}
##LOC[OK]##
##LOC[Cancel]##
{1}
##LOC[OK]##
##LOC[Cancel]##
Home Page
About University
Name And Address
Acedemic Authorities
General Discription
Academic Calendar
General Admission Requirements
Recognition of Prior Learning
General Registration Procedures
ECTS Credit Allocation
Academic Guidance
Information For Students
Cost Of Living
Accommodation
Meals
Medical Facilities
Facilities for Special Needs Students
Insurance
Financial Support for Students
Student Affairs
Learning Facilities
International Programs
Language Courses
Internships
Sports Facilities and Leisure Activities
Student Associations
Practical Information for Mobile Students
Degree Programmes